Most issues with system link play are caused by differences between the logged in player accounts. The in-game troubleshooting messaging is not clear in this case. You may see the players listed in the lobby, but aren't able to join or start a game.

To fix this, all player accounts HAVE to be running the same version of Halo 3. To do this, make sure that all player accounts have once signed in and started up Halo 3 to update the info.